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CHAPTER 1
BACKGROUND OF STUDY
1.1 BACKGROUND OF PNEUMATIC ARTIFICIAL MUSCLE:
According to Catalin CHIVU (2007)
Pneumatic Artificial Muscle (PAM) was an actuator that used air pressure to operate. The use of
this actuator is not rally wide compare to pneumatic cylinder actuator. Pneumatically actuator
artificial muscle represent a relatively recently developed and utilized element in the pneumatic
drives of a mechanical system. A PAM is a system employing a contracting membrane that
under the action of air pressure increases its diameter while decreasing its length. Researchers
from the Orthopaedic Centre of Heidelberg in 1948, the pneumatically actuated arm developed
by the American J.L. McKibben, the stepping robot WAP 1 developed by the Waseda University
of Tokyo (1969) or pneumatic membranes built by the AI Research Centre of Karlsruhe,
Germany (2002) [1]. Pneumatic muscles have been commercialized by the Bridgestone Rubber
Company of Japan since 1980, and more recently, by the U.S. Shadow Robot Company and the
FESTO Corporation of Germany.
1.2 BACKGROUND OF THESIS:
Basically this thesis started on the first month of the year during the first semester. The thesis
basically continues to the 2nd semester from the 1st semester. During the period the following are
the objective achieve:
1.2.1 First Semester Objective achieved:
Identify the literature review for the PAM
Be familiar with the theoretical Equation
1
1.2.2 Second Semester Objective achieved:
Construct a model in Ansys Software
Finish the analysis in the software using Finite Element Analysis.
From the period onward, the analysis of the PAM was move on to the ANSYS Software
using finite element in Neo-Hookean analysis. A model in Ansys was constructed by using
L= 140 mm and D = 20mm
1.3 PROBLEM STATEMENT:
The PAM encountered a nonlinear behavior of a spring itself. Thus, when finite
element analysis apply to the structure of a PAM, it underwent pressure
correspond to its deformation. However, the result was not exact with theoretical
calculation which was linear.
The material type of neoprene rubber must be accurate in order to have the
desired result of deformation.
The PAM supposed to have air pressure inserted into the neoprene rubber. So, a
pressure was applied outward to the surface of the PAM.
1.4 OBJECTIVE:
Analyze the nonlinearity behavior of Pneumatic Artificial Muscle.
Construct a model of Pneumatic Artificial muscle and then go through the
analysis process using Ansys software using Finite Element Analysis.
1.5 SCOPE OF STUDY:
Manufacturing Engineering
Computer Aided Engineering Design
Introduction to Material and Science Engineering
2
CHAPTER 2
LITERATURE REVIEW
2.1 CONCEPT AND OPERATION
Pneumatic muscle is actuating elements that transform pneumatic energy into mechanical
energy. A characterization of the behavior and the performances of these actuating elements
entail both analytical calculations and thorough experimental research. In order to determine the
functional characteristics of a pneumatic muscle, first it structure needs to be explored.
A pneumatic muscle includes an interior tube of various length made from elastic material,
typically silicone rubber or neoprene rubber. This tube is wrapped in a multi-layer nylon fiber
ensuring its strength and protection from the influence of working environment. The behavior of
the pneumatic muscle is similar to that of a spring, meaning that for a completed maximum
stroke the generated force is equal to zero. Pneumatic muscle usually operates at an
overpressure: generating and supplying compressed gas is easier to accomplish and, with
ambient pressure mostly at about 100kPa, a lot more energy can be conveyed by overpressure
than by under pressure. Charging an overpressure, pneumatic muscle with pressurized gas
enables it to move a load, discharging it, conversely, make yield to a load [2].
To see how the pneumatic muscle works, two experiments being conducted. PAM is operated by
gas pressure and is contractile naturally upon inflation. Their construction material simply
consist of a flexible inflatable membrane, reinforced with fibrous filament and fitted with gas
closure fitting for mechanical load-carrying at its ends. As the membrane is pressurized, it bulges
outward in the radial direction, whilst contracting in length along is axial direction. It is during
this axial contraction where PAM exerts a pulling force on its end-effectors. This force generated
from contraction and the subsequent motion on the loads moved is unidirectional. This
differentiates PAM from other pneumatic devices like the bellows, which extends in length when
pressurized. PAM sourced of energy comes from the pressurized gas, usually air, which is forced
3
into the membranes. This pressurization creates a gauge pressure or differential pressure, which
simply means the difference between the air pressure inside the membrane and that of the
ambient atmospheric pressure outside the membrane. Therefore, a PAM is in fact powered by
gauge pressure or differential pressure to carry load. To understand the characteristic of PAM,
two simple experiments can be reviewed.
Experiment 1, consider a mass M hanging at one end on PAM which is fixed on the other end.
The gauge pressure is increased from initial value of zero. At zero gauge pressure, the enclosed
volume is Vmin and the length is maximum which Lmax. As the gauge pressure in the muscle is
increased to a value P1. The enclosed volume is now V1, bulging radially, as the overall lengths
begins contracting, generating a pulling force on the mass M lifting it upwards until force
equilibrium achieved, i.e., when the generated pulling force reaches the value of Mg, g =
gravitational constant, 9.81 m/s2. A further increase in pressure to P2, increases the enclosed
volume to V2, lifting the mass M further upwards by newly generated pulling force. This
experiment revealed two obvious characteristics of PAM. Firstly, PAM shortens in length by
increasing its enclosed volume and secondly, it will contract against a constant load as pneumatic
pressure is gradually increased refer from Frank Daeden and Dirk Lefeber. (2006)
FIGURE 2.1: PAM operation at constant load
4
Experiment 2 setup will be reviewed for another characteristic of PAM. This time the gauge
pressure is kept at a constant value, while the mass will be reduced from the initial value of that
consists of 2 masses. As the mass is reduced to 1 mass, the PAM shortens, while increasing its
enclosed volume. As all mass completely removed, the bulging goes to its full extent, PAM
shortens to a minimal length Lmin and the pulling force will drop to zero. At this point, there is no
more contraction is possible on the PAM. Further, deduction can be added to the existing PAM
characteristic. Firstly, PAM contracts in length under constant pressure as loading is reduced and
secondly, it reaches an optimal point at which no more contraction is possible and the pulling
force subsequently falls to zero, under maximum enclosed volume. Based on both the
experiments carried out and the four characteristics observed, a fifth characteristic can be derived
which is for each configuration of applied pressure and attached pulled load, there exists an
equilibrium length on the PAM, exhibiting s spring-like behavior according to Frank Daeden and
Dirk Lefeber. (2006)
FIGURE 2.2: PAM operation at constant pressure
5
2.2 MCKIBBEN MUSCLE
FIGURE 2.3: Constructed Pneumatic Artificial Muscle
Figure 2.4: Dimension Involves at the PAM according to Catalin CHIVU (2007)
6
This type of pneumatic artificial muscle is the most frequently used and published about at
present. It is a cylindrical braided muscle that has both its tube and its sleeving connected at both
ends to fittings that not only transfer fiber tension but also serve as gas closure. Typical materials
used are latex and silicone rubber and Nylon fibers. By changing its pitch angle the braid
changes its length and diameter. Notating ls as the length of each strand of the braid and N the
amount of encirclements it makes about the tube, one can easily deduce the volume enclosed by
the diaphragm:
V=ls
4 π N2 cosθ sin2 θ (1)
F=−p dvdl (2)
Maximum volume is thus attained at a weave angle of about 54.7°. Increasing the angle beyond
this value is only possible by axially compressing the muscle. This will not be considered as it is
not stable: the flexible muscle shell has no flexural stiffness and thus it would immediately
buckle. When stretching, the pitch angle decreases to a lower limit, which is determined by fiber
thickness, the amount or density of fibers, the number of encirclements and the diameter of the
end fittings. Typical values of pitch angles, given by Caldwell et al. [6], are 59.3° for the
maximum inflation state and 20.0° for the fully stretched state. Tension can be related to weave
angle using (2):
F=π Dmax
2
4(3cos2θ−1) (3)
with Dmax the muscle's diameter at a braid angle of 90°, which is the limiting case. Defining
contraction as
7
ε = 1-llo
(4)
where l stands for muscle actual length and l0 muscle length at rest, tension can also be related to
contraction [14, 23]:
F = π Do
2 p4
( 3tan2θo
(1−ε )2− 1sin2 θo
) (5)
With D0 and θO the diameter and the weave angle at rest, respectively. The state of rest is
determined by the original tube size and braid characteristics. Elongation beyond the rest size is
possible, as stated before, until the minimum pitch angle is reached. The range of contraction-
extension depends on the lower pitch angle limit and, consequently, on the density of strands in
the weave and on their thickness. The tension expressions can be expanded to take into account
friction between sleeving strands and tube and between the strands themselves and deformation
of the inner tube [7]. Friction and non-elastic deformation of the diaphragm will show up as
hysteresis and threshold pressure (i.e. the pressure difference to be exceeded in order to start
radial diaphragm deformation), while elastic lateral deformation will lower tension. The force
needed to elongate or compress the tube with regard to its rest length can be modeled as a
passive spring force acting in parallel with the active force calculated by equation (1). This
passive force will increase tension at l > l0 and lower it at l < l0.
As mentioned earlier, this type of muscle is the most frequently encountered one to date. The
main reason for this seems to be its simple design, ease of assembly and low cost. On the other
hand life expectancy of this muscle, of which no written reports were found, seems not very
high. Users complain about early braid fiber failure at the point of clamping. A major
disadvantage of the McKibben Muscle is its inherent dry friction and threshold pressure. Because
of these, accurate position control is difficult to achieve.
8
2.3 THEORY
During operation L, D and θ are variable (θ changes as length L changes),
L = b cosθ (6)
D = b sin θnπ (7)
The volume of any cylinder is equal to its length times the cross sectional area.
V = π D2
4L (8)
Substituting equations (6), (7) into (8) results
V = b3
4 π n2 sin2 θ cosθ (9)
The maximum contracted length (minimum length) occurs when the actuator volume is at its
greatest. This results in equilibrium of the system. To be able to simulate the static model it is
chosen a PAM that has the maximum interweave angle q = 54.7° and the corresponding length
and diameter L = 140 mm, D = 15 mm. These value together the hypothesis that b and n
parameters are constant during operation, are used to determine this functional parameters. Thus,
from equation (6) results:
b= Lcosθ
= 140cos54.7o =242.27 mm
n=b sinθπD
=242.27· sin 54.7o
π· 15=4.196
0.196 x 100 = 19.6%≈ 20 %
Thus it is obtained that a single threat has 4 complete turns and 20% from the fifth.
9
F=−PgdVDL (10)
Using the geometry that was established above (equations (1) ÷ (3)), can be developed an
equation for force as a function of pressure and interweave angle.
F=−Pg
dVdθdLdθ
=Pg b2(2 cos2θ−sin2 θ)
4 π n2 (11)
Thus, results an equation of force as function of Pg and θ.
F=Pg b2(3cos2θ−1)
4 π n2 (12)
Pg = gauge pressure, kPa
n = number of turn in single thread
θ = interweave angle
F = Force output produce, N
The table below show the relation between length and force theoretically when apply two
pressure values to the PAM into the equation (12):
Length (mm)
Pressure (kPa)100 200
80 5784.32 11568.64
90 7320.78 14641.56
100 9038.00 18076.00
110 10935.98 21871.96
120 13014.72 26029.44
130 15274.22 30548.44
140 17714.48 35428.96
10
TABLE 2.1: Length and Pressure
80 90 100 110 120 130 1400
5000
10000
15000
20000
25000
30000
35000
40000
100200
FIGURE 2.5: Nonlinear PAM behavior of function of F with respect to Length when 100 n 200
kPa pressure applied
The graph above shows the nonlinearity of Force with respect to the length displacement. The
red line indicating the pressure set at 200kpa. Meanwhile the blue line indicating 100kpa
pressure applied.
From this two plots, we can observe that the pattern of the line was nonlinear. This is because the
the material is a neoprene rubber which exhibit the spring like characteristics. The force that
produced shows high value, meaning that pneumatic muscle can produce high force to weight
ratio. So the pneumatic muscle can produce high force with low weight.
11
CHAPTER 3
METHODOLOGY
3.1 GAANT CHART/ PROJECT MILESTONE
Analysis of Pneumatic Artificial M uscle and Construction of a Model
12
AcitivityDuration
Jan Feb
Mar Apr May June July Aug Sept Oct
Nov Dec
First Semester1. Understand the basic concept of PAM
2. Study the PAM working principle
3. Understand the theoretical equation
Second Semester1. Identify the exact material type of
membrane use for PAM2. Understand the Finite Element Analysis
3. Construct a PAM model in Ansys Software
4. Undergo Finite Element Analysis to show the structure deformation when load apply
5. Final Report Writing
3.2 PROJECT PLANNING
Fail
13
Start
Detail Research
Gather dimension and material properties for membrane muscle
Construct the model in Ansys software and apply material properties as well as
loads to the muscle.
Result of deformation of the muscle and Graph of
Iteration Pressure are obtain
End
Pass
3.3 STEPS ANALYSIS
3.3.1 OUTLINE of METHODOLOGY IN THE ANALYSIS ANSYS SOFTWARE
1. DEFINE UNITS
2. MODEL GEOMETRY
3. MESHING
4. PRESSURES APPLY
3.3.2 DEFINE UNITS
The analysis started by defining the units to be used for the analysis. All the define unit
shown in table 3.1:
Unit System Metric (mm, kg, N, °C, s, mV, mA)
Angle Degrees
Rotational Velocity rad/s
Pressure Mpa
TABLE 3.1: Define Unit
3.3.3 MODEL GEOMETRY
A Model geometry being setup that meet specific dimension which is Length = 140mm
and Diameter, D = 20mm. A detail specification shows below in Table 3.2 and 3.3. The
Bounding box dimension is bigger than the radius of the muscle which is 10mm to have
the space for the deformation to take place. Table 3.2 shows the material data properties
to be inserted in material specification in Neo-Hookean analysis
14
Neoprene Rubber > Neo-Hookean > Neo-Hookean
Initial Shear Modulus Mu MPa 2.72e-002
Incompressibility Parameter D1 1/MPa 1.4716e+005
TABLE 3.2: Neoprene Rubber Neo-Hookean Material Property
Model > Geometry
Object Name Geometry
State Fully Defined
Definition
Source C:\Users\skycrapperz\Documents\Project1.agdb
Type DesignModeler
Length Unit Millimeters
Element Control Program Controlled
Display Style Stiffness Behavior
Bounding Box
Length X 39.882 mm
Length Y 39.882 mm
Length Z 140. mm
Properties
Volume 1.7489e+005 mm³
15
Mass 0. kg
Statistics
Bodies 1
Active Bodies 1
Nodes 3335
Elements 665
Preferences
Import Solid Bodies Yes
Import Surface Bodies Yes
Import Line Bodies Yes
Parameter Processing Yes
Personal Parameter Key DS
CAD Attribute Transfer No
Named Selection Processing No
Material Properties Transfer Yes
CAD Associativity Yes
Import Coordinate Systems No
Reader Save Part File No
Import Using Instances Yes
Do Smart Update No
16
Attach File Via Temp File No
Analysis Type 3-D
Mixed Import Resolution None
Enclosure and Symmetry Processing Yes
TABLE 3.3: Model Geometry Specification
Model > Geometry > Parts
Object Name Solid
State Meshed
Graphics Properties
Visible Yes
Transparency 1
Definition
Suppressed No
Material Neoprene Rubber
Stiffness Behavior Flexible
Nonlinear Material Effects Yes
Bounding Box
Length X 39.882 mm
17
Length Y 39.882 mm
Length Z 140. mm
Properties
Volume 1.7489e+005 mm³
Mass 0. kg
Centroid X -2.9458e-016 mm
Centroid Y 4.2082e-016 mm
Centroid Z 70. mm
Moment of Inertia Ip1 0. kg·mm²
Moment of Inertia Ip2 0. kg·mm²
Moment of Inertia Ip3 0. kg·mm²
Statistics
Nodes 3335
Elements 665
TABLE 3.4: Geometry Parts
3.3.4 MESHING
After the model geometry completed, a mesh must be apply to the model in order to show
the structure of muscle before and after the deformation. The Table 3.5 below shows the
characteristic of the mesh applied.
18
Model > Mesh
Object Name Mesh
State Solved
Defaults
Physics Preference Mechanical
Relevance 0
Advanced
Relevance Center Coarse
Element Size Default
Shape Checking Standard Mechanical
Solid Element Midside Nodes Program Controlled
Straight Sided Elements No
Initial Size Seed Active Assembly
Smoothing Low
Transition Fast
Statistics
Nodes 3335
Elements 665
TABLE 3.5: Meshing
19
Figure 3.3: Meshed Pneumatic Muscle Model
3.3.5 STRUCTURAL ANALYSIS
There are a few analyses that can be used in Ansys such as
Static Structural
Flexible Dynamic
Rigid Dynamic
Harmonic response
Linear Buckling
For this project, Static Structural analysis applied to the muscle. The analysis can show
the deformation of the muscle before and after pressures apply into the muscle. More it
enables the properties of material for nonlinear material to be inserted and use for this
analysis. The Table 3.6 shows the characteristic of the analysis and Table 3.7 shows the
setting set in the analysis.
20
Model > Analysis
Object Name Static Structural
State Fully Defined
Definition
Physics Type Structural
Analysis Type Static Structural
Options
Reference Temp 30. °C
TABLE 3.6: Analysis
Model > Static Structural > Analysis Settings
Object Name Analysis Settings
State Fully Defined
Step Controls
Number Of Steps 1.
Current Step Number 1.
Step End Time 5. s
Auto Time Stepping Program Controlled
Solver Controls
Solver Type Program Controlled
Weak Springs Program Controlled
Large Deflection On
21
Inertia Relief Off
Nonlinear Controls
Force Convergence Program Controlled
Moment Convergence Program Controlled
Displacement Convergence
Program Controlled
Rotation Convergence Program Controlled
Line Search Program Controlled
Output Controls
Calculate Stress Yes
Calculate Strain Yes
Calculate Results At All Time Points
Analysis Data Management
Solver Files DirectoryC:\Users\skycrapperz\Documents\Project1 Simulation Files\Static Structural\
Future Analysis None
Save ANSYS db No
Delete Unneeded Files Yes
Nonlinear Solution Yes
TABLE 3.7: Analysis Settings
22
3.3.6 APPLY PRESSURES
Pressure 1 is applied to the muscle at the surface end of the muscle for 2kpa increment
until it reaches 10kpa. Then, pressure 2 of 100kpa is being applied to the surface of the
muscle. The following Table 3.8 and Table 3.9 show the characteristic of it.
Model > Static Structural > Loads
Object Name Pressure 1 Pressure 2 Fixed Support
State Fully Defined
Scope
Scoping Method Geometry Selection
Geometry 2 Faces 1 Face
Definition
Define By Normal To Vector
Type Pressure Fixed Support
Magnitude Tabular Data 1.e-001 MPa (ramped)
TABLE 3.8: Load Value
Steps Time [s] Pressure [MPa]
1
1. 2.e-003
2. 4.e-003
3. 6.e-003
4. 8.e-003
5. 1.e-002
23
TABLE 3.9: Tabulated Pressure 1 Data
CHAPTER 4
RESULT AND DISCUSSION
4.1 Construction of Basic Conceptual Model ( Finite Element Analysis)The result shows the steps in producing a PAM model using Ansys Workbench Software.
Loads were applied to the PAM with constant pressure of 100kpa.
Figure 4.1: Model Geometry of PAM before implementing pressures
Figure 4.2: Model Geometry of
PAM after implementing pressures
24
4.2 Solution Specification
Model > Static Structural > Solution
Object Name Solution
State Solved
Adaptive Mesh Refinement
Max Refinement Loops 1.
Refinement Depth 2.
TABLE 4.1: Solution
Model > Static Structural > Solution > Solution Information
Object Name Solution Information
State Solved
Solution Information
Solution Output Solver Output
Newton-Raphson Residuals 0
Update Interval 2.5 s
Display Points All
TABLE 4.2: Solution Information
Model > Static Structural > Solution > Results
Object Name Total Deformation
State Solved
25
Scope
Geometry All Bodies
Definition
Type Total Deformation
Display Time 5. s
Results
Minimum 0. mm
Maximum 50.89 mm
Information
Time 5. s
Load Step 1
Substep 1
Iteration Number 5
TABLE 4.3: Results
26
Model > Static Structural > Pressure 1
FIGURE 4.3: Pressure 1 vs Time
Model > Static Structural > Pressure 2
FIGURE 4.4: Pressure 2 vs Time
27
After the solution being applied to the muscle, a deformation of the muscle occur that the
length of the muscle decrease when pressure applied to the muscle. As the muscle
decreased in length, the diameter of the muscle increased. So the objective of this project
achieved to prove the behavior of pneumatic muscle after the pressures being applied.
Figure 4.5 shows a nonlinear graph of stress vs strain that act when the muscle starts to
experience pressure at the faces of the muscle. The graph explains the biaxial value is
higher than uniaxial and shear fit. Thus, it proves the pneumatic muscle to have the stress
distributed does not linear with strain. While the Figure 4.6 shows the linearity of
displacement with respect to time. The plot indicates that the length of the PAM linearly
deformed with respect to time.
Neoprene Rubber > Neo-Hookean
FIGURE 4.5: Stress vs Strain Neo-Hookean
28
Figure 4.6: Graph of Displacement vs Time
4.3 Discussion
The artificial muscle reacts towards pressure applied to it and has nonlinear behavior towards
length. The muscle must in different shape as it volume was expanding by applying the pressure
at the surfaces of muscle area. Choosing a right element type and material properties is crucial to
have the accurate result as neo-Hookean value of initial shear modulus needs to accurately
follow the material type of neoprene rubber properties.
More, the incompressibility property needs to be well defined to show the exact behavior of the
muscle when pressures were applied to it. For the result, the muscle should be expanding in
volume with corresponding shortens of length. The Figure 4.5 shows the stress and strain that are
nonlinear towards each other. This proved the characteristic of the muscle nonlinearity.
From the theoretical result shows the graph of Force with respect to length at two applied
pressure. There, it proves that PAM producing large amount of force during its operation
compare to a normal pneumatic cylinder in the market nowadays. From the initial model
geometry, the PAM model deformed in expanding its volume and decreasing its length after
pressures applied to the PAM.
29
CHAPTER 5
CONCLUSION
As for the conclusion, this thesis has successfully proved the nonlinearity of Pneumatic Artificial
Muscle. The PAM increases its volume when inflated after pressures being implemented and
also the length of the muscle decreases. The PAM also have been shown an impact in force –to-
weight ratio as the force produce is high in value compare to its light weight. Thus, the
performance of PAM is higher than normal pneumatic cylinder that produces high force with
high weight. So, PAM is more preferable.
Although PAMs have been around for quite some time now, these actuators have not been
widely used to date, which is not easily explained for. Possible reasons are the lack of large-scale
need for this specific type of actuator and resulting from this a lack of technological effort to
improve the existing designs.
5.1 Recommendation
PAMs have never really been commercially produced, except for the Rubbertuators, which were
manufactured and marketed by Bridgestone Co. for some time. At the present, McKibben-like
muscles are being brought to the market by Festo Ag. & Co. showing a general renewed interest
in these devices. PAMs, nowadays, are mainly used as robotic actuators in applications where
compliance and low power to weight ratio are important e.g. walking/running machines or even
humanoid robots.
However, the PAM is just mainly focused on robotics industry nowadays. So, PAM not really
being applies into the medical industry yet. So the introduction of PAM to the industry can make
a huge different in term of technology and also it might save a lot more people. Thus the effort in
improvement by the medical industry must be highly priority as the benefits of PAM might be
worth explored.
30
REFERENCES
1. Saeed Moaveni, 2008, FINITE ELEMENT ANALYSIS (Theory and Apllication
with Ansys), Third Edition. Pearson International Edition.
2. Ahmad Luqman Al-Hakim , 25th June 2010, Interim Report FYP 1 Pneumatic
Artificial Muscle, University Technology of PETRONAS, Malaysia
3. Deaconescu, A. & Deaconescu, T. 24-26th April 2008, Contribution To The
Behavioural Study of Pneumatically Actuated Artificial Muscle, 6th International
DAAAM Baltic Conference, Industrial Engineering, Tallin, Estonia.
4. Catalin CHIVU, 25-26th October 2007, Static Model and Simulation of A Pneumatic
Artificial Muscle, “Transilvania” University of Brasov, Romania.
5. Frank Daeden, Dirk Lefeber, 2006 Penumatic Artificial Muscle: Actuators for
Robotics and Automation, University of Brussel, Department of Mechanical
Engineering.
6. D.G.Caldwell, G. A. Medrano-Cerda and M.J Goodwin, 1995 Control of Pneumatic
Muscle Actuators, IEEE Control System Magazine, Vol. 15, number 1,pp.40-48,.
7. H. F. Schulte, “The Characteristics of the Mckibben Artificial Muscle”. The
Appication of External Power In Prostheticsand Orthotics, pp-94-115, National of
Academy Science-National Research Council, Publication 874, Lake Arrowhead,
1961.
8. S, Rajendran and D.Q.Song, 11-13th Nov 1998, Finite Element Modelling of
Delamination Buckling of Composite Panel Using ANSYS, Material Technology
Application Centre, Singapore.
31
9. D. B. Reynolds, 24th July 2002, Modelling the Dynamic Characteristics of Pneumatic
Muscle, Annals of Biomedical Engineering, Vol. 31,pp.310-317.
10. R. Ramasamy, M.R.Juhari, 2005, An Application of Finite Element Modelling to
Pneumatic Artificial Muscle, DAG Technology Sdn.Bhd, Malaysia.
11. Keith E. Gordon, 20th May 2005, Mechanical Performance of Artificial Pneumatic
Muscle to Power An Ankle-Foot Orthosis, Journal of Biomechanics.
12. Matthew Wadham-Gagnon, 2007, Hyperelastic Modelling of Rubber In Commercial
Finite Element Software (ANSYS), Industriel, Sherbrooke, Québec, J1L 2T9, Canada.
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McKibben Artificial Pneumatic Muscle Using Flatness Porperty of The System.,
Department of Electrical and Computing Engineering INSA Toulouse, Campus
Scientifique de Rangueil 31077 Toulouse, FRANCE
14. Nguyen Huu Chuc, 12-17th May 2009, Muiti-Jointed Robot Finger Driven by
Artificial Muscle Actuator, Kobe International Conference Center Kobe, Japan
15. Lanka Udawatta and PGS Priyadarshana, 2009, Control of Pneuamtic Artificial
Muscle for Bisep Configuration Using IBC, Department of Electrical Engineering,
University of Moratuwa, Sri Lanka.
32
APPENDIX 1
McKibben Pneumatic Artificial Muscle with Nylon Braided
33
APPENDIX II
McKibben Pneumatic Artificial Muscle with Carbon-Steel Braided
34